Problem: Divide. Write your answer in simplest form. $ \dfrac{9}{7} \div \left(-\dfrac{9}{5}\right) = {?} $
Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $-\dfrac{9}{5}$ is $-\dfrac{5}{9}$. Therefore: $ \dfrac{9}{7} \div \left(-\dfrac{9}{5}\right) = \dfrac{9}{7} \times \left(-\dfrac{5}{9}\right) $ $ \phantom{\dfrac{9}{7} \div \left(-\dfrac{9}{5}\right)} = \dfrac{9 \times (-5)}{7 \times 9} $ $ \phantom{\dfrac{9}{7} \div \left(-\dfrac{9}{5}\right)} = -\dfrac{45}{63} $ Simplify: $ -\dfrac{5}{7}$